title: Exactly solvable chaos in an electromechanical oscillator.
abstract: A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.
authors.affiliation: Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Benjamin A M
authors.initials: BA
authors.lastname: Owens
authors.forename: Mark T
authors.initials: MT
authors.lastname: Stahl
authors.forename: Ned J
authors.initials: NJ
authors.lastname: Corron
authors.forename: Jonathan N
authors.initials: JN
authors.lastname: Blakely
authors.forename: Lucas
authors.initials: L
authors.lastname: Illing